Under a gravitational field, solid particles of hard (metals, semiconductors and oxides) or soft matter (colloids, macromolecules and biological materials) are inhomogeneously distributed along the vertical direction: This process is called sedimentation. Key early advances include the discovery of sedimentation-diffusion equilibrium by Jean Perrin one century ago [1]}, where the number density \(\rho \)  as a function of height \(z\)  is given by [2]} \(P(z)/k_{\rm B}T=\frac{1}{l_{\rm g}}\int _{z}^{h}\rho (z)dz\) , where \(P(z)\)  is the (osmotic) pressure, \(k_{\rm B}\)  is Boltzmann's constant and \(T\)  is temperature. Sedimentation may be characterised by the gravitational length \(l_{\rm g}=k_{\rm B}T/mg\) , where \(m\)  is the buoyant mass of the colloidal particle and \(g\)  is the gravitational acceleration. \(l_{\rm g}\)  may be recast as a Peclet number (\(Pe=\tau _{\rm D}/\tau _{\rm S}\) ), the ratio between the time \(\tau _{\rm D}\)  it takes a particle to diffuse its own radius and the time \(\tau _{\rm S}\)  to sediment its own radius. The Peclet number characterises the colloidal (\(Pe\lesssim 1\) ) and granular limit (\(Pe\gg 1\) ). An isolated spherical particle of diameter \(\sigma \)  settles under gravity, at an average (Stokes') velocity \(u_0=\frac{mg}{3\pi \eta \sigma }\) . Here \(m=\delta \rho \pi \sigma ^{3}/6\)  with \(\delta \rho \)  the mass density difference between colloids and solvent and \(\eta \)  the viscosity of the solvent. This leads to \(u_0\sim \sigma ^{2}\) : Larger particles sediment faster.
